diff --git a/utbot-framework-test/src/test/kotlin/org/utbot/framework/minimization/MinimizationGreedyEssentialTest.kt b/utbot-framework-test/src/test/kotlin/org/utbot/framework/minimization/MinimizationGreedyEssentialTest.kt
index 993f23059a..2a96a677de 100644
--- a/utbot-framework-test/src/test/kotlin/org/utbot/framework/minimization/MinimizationGreedyEssentialTest.kt
+++ b/utbot-framework-test/src/test/kotlin/org/utbot/framework/minimization/MinimizationGreedyEssentialTest.kt
@@ -68,4 +68,18 @@ class MinimizationGreedyEssentialTest {
         val minimizedExecutions = GreedyEssential.minimize(executions)
         assertEquals((1..size).toList(), minimizedExecutions.sorted())
     }
+
+    @Test
+    fun testExecutionPriority() {
+        val executions = mapOf(
+            0 to listOf(0, 1, 2, 3, 4),
+            1 to listOf(0, 1, 2, 3, 4)
+        )
+        val executionToPriority = mapOf(
+            0 to 1,
+            1 to 0
+        )
+        val minimizedExecutions = GreedyEssential.minimize(executions, executionToPriority)
+        assertEquals(listOf(1), minimizedExecutions)
+    }
 }
\ No newline at end of file
diff --git a/utbot-framework/src/main/kotlin/org/utbot/framework/minimization/GreedyEssential.kt b/utbot-framework/src/main/kotlin/org/utbot/framework/minimization/GreedyEssential.kt
index bbbcafd17f..4f229e3712 100644
--- a/utbot-framework/src/main/kotlin/org/utbot/framework/minimization/GreedyEssential.kt
+++ b/utbot-framework/src/main/kotlin/org/utbot/framework/minimization/GreedyEssential.kt
@@ -10,7 +10,8 @@ private inline class LineNumber(val number: Int)
  * [Greedy essential algorithm](CONFLUENCE:Test+Minimization)
  */
 class GreedyEssential private constructor(
-    executionToCoveredLines: Map<ExecutionNumber, List<LineNumber>>
+    executionToCoveredLines: Map<ExecutionNumber, List<LineNumber>>,
+    executionToPriority: Map<ExecutionNumber, Int>
 ) {
     private val executionToUsefulLines: Map<ExecutionNumber, MutableSet<LineNumber>> =
         executionToCoveredLines
@@ -23,8 +24,11 @@ class GreedyEssential private constructor(
             .mapValues { it.value.toMutableSet() }
 
     private val executionByPriority =
-        PriorityQueue(compareByDescending<Pair<ExecutionNumber, Int>> { it.second }.thenBy { it.first.number })
-            .apply {
+        PriorityQueue(
+            compareBy<Pair<ExecutionNumber, Int>> { executionToPriority[it.first] }
+                .thenByDescending { it.second }
+                .thenBy { it.first.number }
+        ).apply {
                 addAll(
                     executionToCoveredLines
                         .keys
@@ -89,12 +93,16 @@ class GreedyEssential private constructor(
          *
          * @return retained execution ids.
          */
-        fun minimize(executions: Map<Int, List<Int>>): List<Int> {
+        fun minimize(executions: Map<Int, List<Int>>, executionToPriority: Map<Int, Int> = mapOf()): List<Int> {
             val convertedExecutions = executions
                 .entries
                 .associate { (execution, lines) -> ExecutionNumber(execution) to lines.map { LineNumber(it) } }
 
-            val prioritizer = GreedyEssential(convertedExecutions)
+            val convertedExecutionToPriority = executionToPriority
+                .entries
+                .associate { (execution, priority) -> ExecutionNumber(execution) to priority }
+
+            val prioritizer = GreedyEssential(convertedExecutions, convertedExecutionToPriority)
             val list = mutableListOf<ExecutionNumber>()
             while (prioritizer.hasMore()) {
                 list.add(prioritizer.getExecutionAndRemove())
diff --git a/utbot-framework/src/main/kotlin/org/utbot/framework/minimization/Minimization.kt b/utbot-framework/src/main/kotlin/org/utbot/framework/minimization/Minimization.kt
index d3b2c19918..a34af60f79 100644
--- a/utbot-framework/src/main/kotlin/org/utbot/framework/minimization/Minimization.kt
+++ b/utbot-framework/src/main/kotlin/org/utbot/framework/minimization/Minimization.kt
@@ -18,6 +18,7 @@ import org.utbot.framework.plugin.api.UtModel
 import org.utbot.framework.plugin.api.UtNullModel
 import org.utbot.framework.plugin.api.UtPrimitiveModel
 import org.utbot.framework.plugin.api.UtStatementModel
+import org.utbot.framework.plugin.api.UtSymbolicExecution
 import org.utbot.framework.plugin.api.UtVoidModel
 
 
@@ -53,8 +54,11 @@ fun minimizeExecutions(executions: List<UtExecution>): List<UtExecution> {
         executions.indices.filter { executions[it].coverage?.coveredInstructions?.isEmpty() ?: true }.toSet()
     // ^^^ here we add executions with empty or null coverage, because it happens only if a concrete execution failed,
     //     so we don't know the actual coverage for such executions
-    val mapping = buildMapping(executions.filterIndexed { idx, _ -> idx !in unknownCoverageExecutions })
-    val usedExecutionIndexes = (GreedyEssential.minimize(mapping) + unknownCoverageExecutions).toSet()
+
+    val filteredExecutions = executions.filterIndexed { idx, _ -> idx !in unknownCoverageExecutions }
+    val (mapping, executionToPriorityMapping) = buildMapping(filteredExecutions)
+
+    val usedExecutionIndexes = (GreedyEssential.minimize(mapping, executionToPriorityMapping) + unknownCoverageExecutions).toSet()
 
     val usedMinimizedExecutions = executions.filterIndexed { idx, _ -> idx in usedExecutionIndexes }
 
@@ -143,13 +147,14 @@ private fun <T : Any> groupExecutionsByTestSuite(
     executions.groupBy { executionToTestSuite(it) }.values
 
 /**
- * Builds a mapping from execution id to edges id.
+ * Builds a mapping from execution id to edges id and from execution id to its priority.
  */
-private fun buildMapping(executions: List<UtExecution>): Map<Int, List<Int>> {
+private fun buildMapping(executions: List<UtExecution>): Pair<Map<Int, List<Int>>, Map<Int, Int>> {
     // (inst1, instr2) -> edge id --- edge represents as a pair of instructions, which are connected by this edge
     val allCoveredEdges = mutableMapOf<Pair<Long, Long>, Int>()
     val thrownExceptions = mutableMapOf<String, Long>()
     val mapping = mutableMapOf<Int, List<Int>>()
+    val executionToPriorityMapping = mutableMapOf<Int, Int>()
 
 
     executions.forEachIndexed { idx, execution ->
@@ -169,11 +174,12 @@ private fun buildMapping(executions: List<UtExecution>): Map<Int, List<Int>> {
                     edges += allCoveredEdges[instructions[i] to instructions[i + 1]]!!
                 }
                 mapping[idx] = edges
+                executionToPriorityMapping[idx] = execution.getExecutionPriority()
             }
         }
     }
 
-    return mapping
+    return Pair(mapping, executionToPriorityMapping)
 }
 
 /**
@@ -264,4 +270,15 @@ private fun addExtraIfLastInstructionIsException(
  * Takes an exception name, a class name, a method signature and a line number from exception.
  */
 private fun Throwable.exceptionToInfo(): String =
-    this::class.java.name + (this.stackTrace.firstOrNull()?.run { className + methodName + lineNumber } ?: "null")
\ No newline at end of file
+    this::class.java.name + (this.stackTrace.firstOrNull()?.run { className + methodName + lineNumber } ?: "null")
+
+/**
+ * Returns an execution priority. [UtSymbolicExecution] has the highest priority
+ * over other executions like [UtFuzzedExecution], [UtFailedExecution], etc.
+ *
+ * See [https://github.com/UnitTestBot/UTBotJava/issues/1504] for more details.
+ */
+private fun UtExecution.getExecutionPriority(): Int = when (this) {
+    is UtSymbolicExecution -> 0
+    else -> 1
+}